Related papers: Non-uniform sampled scalar diffraction calculation…
A new method, FM-FTS, combining Frequency Modulation heterodyne laser spectroscopy and Fourier Transform Spectroscopy is presented. It provides simultaneous sensitive measurement of absorption and dispersion profiles with broadband spectral…
We study two discretisations of the nonlinear Fourier transform of AKNS-ZS type, ${\cal F}^E$ and ${\cal F}^D$. Transformation ${\cal F}^D$ is suitable for studying the distributions of the form $u = \sum_{n = 1}^N u_n \, \delta_{x_n}$,…
Single-shot coherent diffractive imaging (CDI) using intense XUV and soft X-ray pulses holds the promise to deliver information on the three dimensional shape as well as the optical properties of nano-scale objects in a single diffraction…
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. So far, various window functions…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…
We outline a novel numerical method, called Ultrafast Ultrafast (UF$^2$), for calculating the $n^\text{th}$-order wavepackets required for calculating n-wave mixing signals. The method is simple to implement, and we demonstrate that it is…
The basic principle of astronomical interferometry is to derive the angular distribution of radiation in the sky from the Fourier transform of the electric field on the ground. What is so special about the Fourier transform? Nothing, it…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
Image computation is a fundamental tool for performance assessment of astronomical instrumentation, usually implemented by Fourier transform techniques. We review the numerical implementation, evaluating a direct implementation of the…
Scattering scanning near-field optical microscopy (s-SNOM) is a technique to enhance the spatial resolution, and when combined by Fourier transform spectroscopy it can provide spectroscopic information with high spatial resolution. This…
The special unitary group SU(2) plays a fundamental role in the description of symmetries in quantum mechanics, theoretical physics, and spherical signal processing. In this paper, we address the computational challenges of performing…
We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic…
Diffusion models are proficient at generating high-quality images. They are however effective only when operating at the resolution used during training. Inference at a scaled resolution leads to repetitive patterns and structural…
The Fourier spectrum at a fractional period is often examined when extracting features from biological sequences and time series. It reflects the inner information structure of the sequences. A fractional period is not uncommon in time…
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…
The common methods of spectral analysis for multivariate ($n$-dimensional) time series, like discrete Frourier transform (FT) or Wavelet transform, are based on Fourier series to decompose discrete data into a set of trigonometric model…
We present a unified treatment of the Fourier spectra of spherically symmetric nonlocal diffusion operators. We develop numerical and analytical results for the class of kernels with weak algebraic singularity as the distance between source…
One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However,…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…